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In this paper, we derived closed form analytical solutions for the effective viscosity of the suspensions of solid spheres that take into account size effects. This result was obtained by using the solution for the effective shear modulus of particulate composites developed in the framework of the strain gradient elasticity theory. Assuming the incompressibility of the matrix and the rigid behavior of particles and using a mathematical analogy between the theories of elasticity and viscous fluids, we derived generalized Einstein's formula for effective viscosity. Then, generalized Brinkman's solution for the concentrated suspensions was derived using the differential method. The obtained solutions contain a single additional length scale parameter, which can be related to the interactions between the base liquid and solid particles in the suspensions. In the case of a large ratio between the diameter of the particles and the length scale parameter, the developed solutions were reduced to the classical solutions. However, for the small relative diameter of particles, an increase of the effective viscosity was predicted. It was shown that the developed models agree well with the known experimental data. Solutions for the fibrous suspensions were also derived and validated. [ABSTRACT FROM AUTHOR]

Solid-solution hardening (SSH), originated mainly from the point obstacles with prescribed resistance (short-range) or spherical inclusions with purely dilatational eigenstrain (long-range), is critical to materials science and technological applications. Dislocation gliding in solid-solution hardening alloys generally undergoes both short-range and long-range interactions. However, the respective contribution of each aspect remains unclear. Here, we successfully decouple the short-range lattice distortion and long-range size misfit of the solid-solution hardening effect by introducing two scaling factors (s1 and s3) and analyzing the contributions of each aspect on the solute/dislocation interaction, respectively. For scaling factor s1, the interaction energy is localized, resembling the short-range interactions without volume change. The scaling factor s3 is equivalent to a dilatation/constriction center with volume change. The interaction energy is a long-range parameter and well predicted from the pure continuum elasticity perspective. Large-scale molecular dynamics (MD) simulations reveal the unique impacts of two strengthening mechanisms on dislocations with different scaling factors. It is found that the energy landscape and size misfit effect of the solute atoms play important roles in the SSH effect. With deeply understanding the SSH effects and the rapidly increasing computational power, it may pave a practical way to apply MD simulations on complex strengthening mechanism studies. [ABSTRACT FROM AUTHOR]

In this paper, we study the elastic properties of the entropy-stabilized oxide (Mg, Co, Ni, Cu, Zn)O using experimental and first principles techniques. Our measurements of the indentation modulus on grains with a wide range of crystallographic orientations of the entropy-stabilized oxide revealed a high degree of elastic isotropy at ambient conditions. First principles calculations predict mild elastic anisotropy for the paramagnetic structure, which decreases when the system is considered to be non-magnetic. When the antiferromagnetic state of CoO, CuO, and NiO is accounted for in the calculations, a slight increase in elastic anisotropy is observed, suggesting a coupling between magnetic ordering and the orientation dependent elastic properties. Furthermore, an examination of the local structure reveals that the isotropy is favored through local ionic distortions of Cu and Zn—due to their tendencies to form tenorite and wurtzite phases. The relationships between the elastic properties of the multicomponent oxide and those of its constituent binary oxides are reviewed. These insights open up new avenues for controlling isotropy for technological applications through tuning composition and structure in the entropy-stabilized oxide or the high-entropy compounds in general. [ABSTRACT FROM AUTHOR]

Using density functional theory combined with an evolutionary algorithm for crystal structure prediction, we study the elastic and electronic properties of various multi-principal element alloys that are based on CoCrFeNi. In total, nine quinary and one senary CoCrFeNiX (X = Ti , V, Mn, MnV, Cu, Zr, Nb, Mo, Al, Al 2) alloys are studied along with the base CoCrFeNi alloy. The aim of the current study is twofold. First, we test and confirm the ability of the presented methodology to predict the crystal structure of the multi-principal element alloys based on Co, Cr, Fe, and Ni elements. Second, we calculate and compare the elastic properties of the CoCrFeNiX alloys, as well as their electronic properties, in an attempt to establish possible correlations between them. Taking CoCrFeNi as the reference alloy, our first-principles calculations of various elastic moduli (bulk, Young, and shear moduli) show that only the bulk moduli of the alloys with Cu, Mo, or Nb (in this order) are expected to be larger. Furthermore, our comparative analysis of the CoCrFeNiX alloys containing partially filled 3 d and 4 d elements shows that the filling of the d -shell causes a general increase in all the elastic moduli. The only exception is the decreasing behavior of the bulk modulus in the case of alloys with partially filled 3 d elements. [ABSTRACT FROM AUTHOR]

Wrinkled surfaces have attracted enormous interest during the past years due to their various wrinkling patterns and impressive multifunctional properties. With the growing demand of numerous potential applications, it is desirable to uncover the formation mechanism and develop fabrication methods for tunable wrinkles, in particular, for hierarchical wrinkle that has spatially varying wavelength and amplitude. In this tutorial, we comprehensively discuss the possible mechanism of the formation of hierarchical wrinkles, including the role of elasticity gradient in film–substrate systems, the effect of boundary confinement, the sequential multistep strain-releasing method in a multilayer system, etc. The formation conditions and morphological features of various hierarchical wrinkling patterns are outlined. Lastly, representative applications of hierarchical wrinkling are briefly summarized as well. [ABSTRACT FROM AUTHOR]

Topological materials are considered as a novel quantum state of matter, which can be characterized by symmetry-protected Dirac interfacial states, and exhibit an exotic phenomenon when combined with the other phases. The topological phase in the perovskite structures is important since it can provide various heterostructure interfaces with multifunctional properties. Alpha-(α-) phase cesium-based halide perovskites CsSnX3 (X = I, Br, Cl) can be considered as a promising candidate for topological semiconductors under hydrostatic pressures. The narrow bandgap of these compounds (≤1.83 eV) has made them interesting materials for the electronic, optoelectronic, and photovoltaic applications. In the current research, we systematically carry out first-principles density functional theory (DFT) to study the effects of hydrostatic pressure on the electronic structure of CsSnX3 (X = I, Br, Cl) compounds. The topological phase of these compositions is investigated using the Fu–Kane and Wilson loop methods in order to identify the Z2 topological invariants for each structure. The topological surface states (TSSs) of the (001) plane of these compounds are investigated using the semi-infinite Green's function. These TSSs guarantee the nontrivial nature of CsSnX3 compounds under pressure. With respect to the engineering applications, three important mechanical properties of these compounds including elastic anisotropy, ductility, and hardness are also investigated. [ABSTRACT FROM AUTHOR]

The lattice thermal conductivity and thermal transport properties of 2D α-selenene are investigated based on the first-principles calculations. The isotropic in-plane thermal conductivity is as low as 3.04 W m−1 K−1 at room temperature, even abnormally lower than α-tellurene that processes analogous configuration and lower Debye temperature. We find this abnormal phenomenon reasonably stems from the larger anharmonicity of the acoustic phonon branch. Moreover, the phonon spectra, elastic properties, and related thermal properties are also exhibited. Acoustic phonons contribute mainly to the total thermal conductivity. Furthermore, size effect, boundary effect, the total phase space for three-phonon processes, phonon group velocity, and relaxation time are further investigated, and the last one is unveiled to be the key ingredient of thermal transport in 2D selenene. [ABSTRACT FROM AUTHOR]

We present an analytical model describing misfit stresses relaxation in semipolar III-nitride heterostructures caused by misfit dislocations (MDs) originating from basal or prismatic slip and by sessile MDs. We analyze the critical thickness hc for the formation of MDs depending on crystal lattice mismatch and orientation of the semipolar growth plane. We explore transversely isotropic elasticity solutions to describe the relaxation processes in III-nitride semipolar heterostructures and compare the results for hc with those calculated within the isotropic elasticity approach. We find that the value of angle ϑ between the polar с-axis, and the direction of heterostructure growth has an impact on the realization of the stress relaxation mechanism by the generation of MDs originating either from basal or prismatic slip. A comparison of theoretical calculations with experimental data on the observation of MDs in the III-nitride heterostructures is provided. [ABSTRACT FROM AUTHOR]

The present paper presents a Bernoulli–Euler flexomagnetic (FM) nanobeam model, which considers the effects of flexomagneticity, piezomagneticity, and the surface elasticity. Differential control equations and corresponding magnetic boundary conditions are derived to investigate the influences of direct and converse FM couplings over the magnetic-elastic response. Size-dependent theoretical solutions for the static bending deformation of the cantilever, simply supported, and clamped nanobeams subjected to concentrated or uniformly distributed load are derived. Numerical simulations demonstrate that the flexomagneticity effect plays the role of the scale-dependent enhancement of the bending rigidity, which is independent of boundary conditions. But for the residual surface stresses, softening or stiffening the beam depends on boundary conditions. [ABSTRACT FROM AUTHOR]

The photogenerated excess carriers' influence on the temperature distribution and thermoelastic photoacoustic signals of n-type silicon excited with a light source of modulated intensity is theoretically investigated for modulation frequencies ranging from 1 to 107 Hz. This is done by comparing the amplitude and the phase of the temperature and photoacoustic signals with and without the presence of excess carriers, giving special attention to the presence of characteristic peaks of the amplitude ratios and phase differences between the signals at the front and rear sample surfaces. It is shown that these peaks can be understood as the fingerprints of the excess carrier presence in the semiconductor. Furthermore, the strong dependence of the temperature distribution on the carrier recombination processes at the surfaces of thin samples is quantified and found to drastically change the thermoelastic component of the photoacoustic signal. [ABSTRACT FROM AUTHOR]

The elastic properties of rare-earth scandates were only reported at room temperature based on simulations and experimental measurements with poor agreement thus far. Using resonant ultrasound spectroscopy and inductive gauge dilatometry, we determined the elastic stiffnesses, their temperature dependence, and thermal expansion coefficients of SmScO 3 , TbScO 3 , and DyScO 3 between 103 K and 1673 K. Our set of elastic stiffnesses shows high internal consistency, e.g., the relations c 11 > --> c 33 > --> c 22 , c 66 > --> c 44 > --> c 55 , and c 13 ≥ c 12 > --> c 23 hold for all crystal species at room temperature. The structures become overall stiffer with decreasing R E -radius and increased charge density. The behavior of c 44 at low temperatures indicates in all R E ScO 3 a structural instability that might lead to an orthorhombic → monoclinic transition involving shear of the (100)-plane upon increasing pressure. The transition seems to be promoted by a decreasing R E -radius. Anomalies in two mixed resistances of TbScO 3 below room temperature are indicative of at least one more structural instability that may also cause a phase transition where the structure is sheared. So far, only magnetic phase transitions at about 3 K have been observed in R E ScO 3 in literature. The thermoelastic properties in [100] and [001] directions of all materials become increasingly isotropic at high temperatures, suggesting decreased structural tilt. (100) or (010) crystal cuts should be chosen for applications of a R E ScO 3 as a substrate material, when mostly isotropic thermal expansion or longitudinal stiffness in-plane is desired, respectively. [ABSTRACT FROM AUTHOR]

The elastic properties of rare-earth scandates were only reported at room temperature based on simulations and experimental measurements with poor agreement thus far. Using resonant ultrasound spectroscopy and inductive gauge dilatometry, we determined the elastic stiffnesses, their temperature dependence, and thermal expansion coefficients of SmScO 3 , TbScO 3 , and DyScO 3 between 103 K and 1673 K. Our set of elastic stiffnesses shows high internal consistency, e.g., the relations c 11 > --> c 33 > --> c 22 , c 66 > --> c 44 > --> c 55 , and c 13 ≥ c 12 > --> c 23 hold for all crystal species at room temperature. The structures become overall stiffer with decreasing R E -radius and increased charge density. The behavior of c 44 at low temperatures indicates in all R E ScO 3 a structural instability that might lead to an orthorhombic → monoclinic transition involving shear of the (100)-plane upon increasing pressure. The transition seems to be promoted by a decreasing R E -radius. Anomalies in two mixed resistances of TbScO 3 below room temperature are indicative of at least one more structural instability that may also cause a phase transition where the structure is sheared. So far, only magnetic phase transitions at about 3 K have been observed in R E ScO 3 in literature. The thermoelastic properties in [100] and [001] directions of all materials become increasingly isotropic at high temperatures, suggesting decreased structural tilt. (100) or (010) crystal cuts should be chosen for applications of a R E ScO 3 as a substrate material, when mostly isotropic thermal expansion or longitudinal stiffness in-plane is desired, respectively. [ABSTRACT FROM AUTHOR]

Hardness and fracture toughness are some of the most important mechanical properties. Here, we propose a simple model that uses only the elastic properties to calculate the hardness and fracture toughness. Its accuracy is checked by comparison with other available models and experimental data for metals, covalent and ionic crystals, and bulk metallic glasses. We found the model to perform well on all datasets for both hardness and fracture toughness, while for auxetic materials (i.e., those having a negative Poisson's ratio), it turned out to be the only model that gives reasonable hardness. Predictions are made for several materials for which no experimental data exist. [ABSTRACT FROM AUTHOR]

The low-energy structures of irradiation-induced defects in materials have been studied extensively over several decades, as these determine the available modes by which a defect can diffuse or relax, and how the microstructure of an irradiated material evolves as a function of temperature and time. Consequently, many studies concern the relative energies of possible defect structures, and empirical potentials are commonly fitted to or evaluated with respect to these. But recently [S. L. Dudarev et al., Nucl. Fusion 58, 126002 (2018)], we have shown that other parameters of defects not directly related to defect energies, namely, their elastic dipole tensors and relaxation volumes, determine the stresses, strains, and swelling of reactor components under irradiation. These elastic properties of defects have received comparatively little attention. In this study, we compute relaxation volumes of irradiation-induced defects in tungsten using empirical potentials and compare to density functional theory results. Different empirical potentials give different results, but some clear potential-independent trends can be identified. We show that the relaxation volume of a small defect cluster can be predicted to within 10% from its point-defect count. For larger defect clusters, we provide empirical fits as a function of defect cluster size. We demonstrate that the relaxation volume associated with a single primary-damage cascade can be estimated from the primary knock-on atom energy. We conclude that while annihilation of defects invariably reduces the total relaxation volume of the cascade debris, there is still no conclusive verdict about whether coalescence of defects reduces or increases the total relaxation volume. [ABSTRACT FROM AUTHOR]

Nanostructure and mechanical properties of bulk nanocristalline cubic boron nitride have been studied by transmission electron microscopy and micro- and nanoindentation. The obtained data on hardness, elastic properties, and fracture toughness clearly indicate that nano-cubic (F 4 ¯ 3 m) boron nitride belongs to a family of advanced ultrahard materials. [ABSTRACT FROM AUTHOR]

First-principles calculations were carried out to investigate electronic structure, phase stability, elastic properties, Debye temperature, and hardness of the TiC–HfC and TiC–TaC random solid solutions as functions of composition. For TiC–HfC, significant miscibility gaps with consolute temperatures about 1975 K are revealed in the binodal and spinodal curves. The negative deviation of the elastic moduli and hardness from linearity are obtained for TiC–HfC, whereas, for TiC–TaC, these characteristics are above their linear interpolation between the end members. Concentration dependences of the Debye temperature for both systems have a negative curvature. To clarify a possible mechanism of stabilization or destabilization of these solid solutions and other similar carbide systems, mixing energies of the M1 1 − x M2 x C alloys, where M1 and M2 are the transition metals of the IV, V, and partially VI groups, were calculated. It is found that the behavior of mixing energies for the M1C–M2C alloys with M1 and M2 of different groups depending on composition is determined by the difference between cell volumes of the end members, Δ V C , the degree of occupancy of the metal band, and the shape of the density of states in the metal band region. Values of Δ V C mainly are responsible for positive mixing energies of the alloys with valence electron concentrations (VECs) equal to 8 and 9 for which occupancy of the metal band weakly changes with composition. The maximum hardness of the solid solutions for which VECs of the end members are different is predicted to be reached for the compositions with VECs = 8.5–8.75. [ABSTRACT FROM AUTHOR]

Temporal-enhanced ultrasound (TeUS) imaging is a recently developed method based on the analysis of US time series. In this report, we show experimentally that the TeUS amplitude is sensitive to scatterer size and their density, as well as to the microvibration amplitude. Since the microvibration amplitude depends on the local elasticity of the medium, TeUS is able to differentiate tissues based on their elasticity, in addition to scatterer density and cross section. It is argued that interference effects, i.e., US speckle, are enhancing the TeUS effect. In this study, ultrasound phantoms were designed to mimic tissues with three different viscoelasticities and three different scatterer sizes. Into each of the nine phantoms, a flexible tubing was embedded and used to generate local microvibrations at 1 Hz and with an amplitude below 20 μm. Time series of raw ultrasound images were analyzed to extract the B-mode intensity, the scatterer displacement, and the shear modulus at a variety of different microvibration amplitudes. [ABSTRACT FROM AUTHOR]

Nonlinear ultrasonic technique is one of several promising nondestructive evaluation methods for monitoring the evolution of nanosized defects such as radiation-induced defects in nuclear materials. In this work, a microstructure-based phase-field model of dynamic deformation in elastically nonlinear materials has been developed for investigating the dynamic interaction between distributed defects and a propagating longitudinal sound wave. With the model, the effect of second phase precipitates' size and properties on the nonlinearity parameter β that describes the magnitude of the 2nd harmonic wave was simulated. The results showed that (1) the nonlinearity parameter β increases as the elastic inhomogeneity increases regardless of whether the precipitates are softer or harder than the matrix; (2) β linearly increases with the increase of lattice mismatch strain; and (3) for a given volume fraction of second phase precipitates, β strongly depends on the precipitate size. The predicted precipitate size dependence of β agrees with the experimental data. These results demonstrate that the developed model enables one to predict the contributions of different nonlinear sources to β , to explain the signal physics behind the measured nonlinear ultrasonic response, and to guide the development of nonlinear ultrasound nondestructive detection of material defects in nuclear reactor materials. [ABSTRACT FROM AUTHOR]

Using first-principles density functional theory calculations, the mechanical and electronic properties of the three main (β12, χ3, and striped) phases of single-layer borophene sheets are calculated under in-plane uniaxial/biaxial strain, including the harmonic strain-energy regions of β12, χ3, and striped phases over the strain ranges of −3.5%–3.5%, −4.5%–4.5%, and −2.5%–2.5%, respectively, along the x direction (the direction of the highest bond orientation). We introduce a method by which the nonlinear behavior of these and any other two-dimensional materials can be investigated even above their ultimate strains, beyond which no-uniform plastic deformation occurs. Defining an appropriate deformation, and utilizing both continuum modeling and special equations based on the density functional theory, a method of computing second-, third-, and fourth-order elastic constants of the three different phases of borophene is presented that utilizes rectangular unit cells, which can substitute for any two-dimensional unit cell. Using this new method, 4 independent second-order, 6 third-order, and 9 fourth-order elastic constants are calculated, which is the complete set of elastic constants for two-dimensional structures. The electronic band structure of borophene shows anisotropic electronic behavior. Despite the metallic character of borophene sheets, applying directional strain based on deformation matrices creates a bandgap in some regions of the Brillouin zones, opening up the possibility of mechanical control of electronic properties. [ABSTRACT FROM AUTHOR]

Mechanical micro- and nano-patterning processes rely on engineering the interactions between a stamp and a substrate to accommodate surface roughness and particle defects while retaining the geometric integrity of printed features. We introduce a set of algorithms for rapidly simulating the stamp–substrate contact, and we use them to show that advantageous behavior can occur when the stamp consists of a finite-thickness layer bonded to a layer with different elastic properties. The simulations use two-dimensional load-response functions describing in discrete space the response of a stamp surface's shape to a localized unit load. These load-response functions incorporate the contributions both of local, indentation-like displacements and of plate-like bending of finite-thickness stamp layers. The algorithms solve iteratively for contact pressure distributions that, when spatially convolved with the load response, yield deformations consistent with the properties of the stamp and the substrate. We investigate three determinants of stamp performance: conformation to sinusoidal substrate topographies, distortion of material around stamp protrusions, and conformation to isolated spherical dust particles trapped between the stamp and the substrate. All simulation results are encapsulated in dimensionless models that can be applied to the efficient selection of stamp geometries, materials, and loading conditions. A particularly striking finding is that a stamp with a finite-thickness compliant coating bonded to a more rigid support can conform more closely to a trapped particle under a given load than a homogeneous stamp with the properties of the coating. This finding could be used to minimize the impact of particle defects on patterning processes. [ABSTRACT FROM AUTHOR]

Elastic constants and their derived properties of various cubic Heusler compounds were calculated using the first-principles density functional theory. To begin with, Cu 2 MnAl is used as a case study to explain the interpretation of the basic quantities and compare them with experiments. The main part of the work focuses on Co 2 -based compounds that are Co 2 Mn M with the main group elements M = Al , Ga, In, Si, Ge, Sn, Pb, Sb, Bi, and Co 2 T M with the main group elements Al or Si, and the 3 d transition metals T = Sc , Ti, V, Cr, Mn, and Fe. It is found that many properties of Heusler compounds correlate to the mass or nuclear charge Z of the main group element. Additional representation and compact simplification of the elastic data is useful to investigate and compare their influence on crystal stability and physical properties. Here, Blackman's and Every's diagrams are used to compare the elastic properties of the materials, whereas Pugh's and Poisson's ratios are used to analyze the relationship between interatomic bonding and physical properties. It is found that Pugh's criterion on brittleness needs to be revised whereas Christensen's criterion describes the ductile–brittle transition of Heusler compounds very well. The calculated elastic properties give hint on a metallic bonding with an intermediate brittleness for the studied Heusler compounds. The universal anisotropy of the stable compounds has values in the range of 0.57 < A U < 2.73. The compounds with higher A U values are found close to the middle of the transition metal series. In particular, Co 2 ScAl with A U = 0.01 is predicted to be an isotropic material that comes closest to an ideal Cauchy solid as compared to the remaining Co 2 -based compounds. Apart from the elastic constants and moduli, the sound velocities, Debye temperatures, and hardness are predicted and discussed for the studied systems. The calculated slowness surfaces for sound waves reflect the degree of anisotropy of the compounds. [ABSTRACT FROM AUTHOR]

To understand crystal anisotropy effects on shock-induced elastic-plastic deformation of molybdenum (Mo), results from high-purity single crystals shocked along [110] and [111] orientations to an elastic impact stress of 12.5 GPa were obtained and compared with the [100] results previously reported [A. Mandal and Y. M Gupta, J. Appl. Phys. 121, 045903 (2017)]. Measured wave profiles showed a time-dependent response, and strong anisotropy was observed in the elastic wave attenuation with the propagation distance, elastic limits, shock speeds, and overall structure of the wave profiles. Resolved shear stresses on {110}〈111〉 and {112}〈111〉 slip systems provided insight into the observed anisotropy in elastic wave attenuation and elastic limits and showed that shear stresses, and not longitudinal stresses, are a better measure of strength in shocked single crystals. Under shock compression, resolved shear stresses at elastic limits were comparable to the Peierls stress of screw dislocations in Mo. Elastic wave attenuation was rapid when shear stresses were larger than the Peierls stress. Large differences in the elastic limits under shock and quasi-static loading are likely a consequence of the large Peierls stress value for Mo. Numerically simulated wave profiles, obtained using the dislocation-based plasticity model described in the [100] work, showed good agreement with all measured wave profiles but could not differentiate between the {110}〈111〉 and {112}〈111〉 slip systems. Overall, experimental results and corresponding numerical simulations for the three crystal orientations have provided a comprehensive insight into shock-induced elastic-plastic deformation of Mo single crystals, including the development of a continuum material model. [ABSTRACT FROM AUTHOR]

In the present study, we examine the surface shear horizontal (SH) wave in a classical linear elastic half-space covered by a surface layer modeled by the couple stress theory [Mindlin and Tiersten, Arch. Ration. Mech. Anal. 11, 415 (1962)]. The boundary conditions on the surface of the half space are translated into the "body" forces in the surface layer according to the surface elasticity proposed by Gurtin and Murdoch [Arch. Ration. Mech. Anal. 57, 291 (1975)]. Combining the surface elasticity and the couple stress theory, we find that the surface SH waves are only available for a limited range of wavelengths due to the presence of the micro-length in the couple stress theory. [ABSTRACT FROM AUTHOR]

Hydrostatic simulations are performed to study Richtmyer-Meshkov instability and jet formation in elastic-plastic Pb under shock wave loading. The effects of yield strength and surface perturbation on perturbation growth and jet formation are investigated. An algebraic relationship between the upper limit of ejecta mass and bubble saturation amplitude for the elastic-plastic solid is revealed, and an analytic expression for the maximum ejecta mass varying with material strength, surface perturbation, and shock conditions is presented based on Richtmyer-Meshkov instability theories for the elastic-plastic medium. [ABSTRACT FROM AUTHOR]

The elastic properties of praseodymium (Pr) were investigated at pressure up to 12 GPa at room temperature using the ultrasonic interferometry technique. Softening and discontinuities in compressional (P) and shear (S) wave velocities were observed at around 2.5, 6.5, and 10.5 GPa, which are interpreted as indications of the phase transitions from Pr-I (dhcp) to Pr-II (fcc), Pr-II (fcc) to Pr-III (d-fcc), and Pr-III (d-fcc) to Pr-VII (monoclinic or orthorhombic), respectively. Discontinuities in compressibility have been observed across the phase transitions of I-II and II-III of Pr by an analysis of pressure derivatives of the elastic moduli. A comparison with the elastic behaviors of other lanthanide elements (e.g., Ce and La) suggests that the elastic anomalies associated with these phase transitions are likely to be caused by the 6s-5d electron transfer and the softening of acoustic phonon mode facilitated by decreased atomic distances under pressure. [ABSTRACT FROM AUTHOR]

We calculate analytically the strain tensor for epitaxial, pseudomorphic heterostructures of arbitrary growth plane for monoclinic and rhombohedral crystals. As numerical examples, we treat heterostructures from sesquioxides, namely, monoclinic (Ga-rich) (Al,Ga) 2 O 3 on β -Ga 2 O 3 and rhombohedral (Al-rich) (Al,Ga) 2 O 3 on α -Al 2 O 3 using realistic material parameters. We predict the strains in laboratory and crystal coordinates and derive properties such as lattice constants and tilt of lattice planes for comparison with X-ray data. Our theory also applies to any higher symmetric structure such as orthorhombic, tetragonal, cubic, and hexagonal heterostructures. [ABSTRACT FROM AUTHOR]

The elastic and plastic deformation of a gold nanowire tested in a three-point bending configuration using the custom-built scanning force microscope SFINX was studied in situ by Laue micro-diffraction. A new data treatment method based on the integration of diffraction patterns recorded along the deformed nanostructure is introduced visualizing both the movement and shape of the diffraction peaks as a function of the measurement position. Besides bending, torsion is evidenced during the elastic deformation originating from a misalignment of the SFINX-tip of the order of 60 nm with respect to the nanowire center. As demonstrated by post-mortem Laue micro-diffraction maps, the plastic deformation is governed by the storage of geometrically necessary dislocations. Analyzing the shape of the diffraction peaks, the activation of two unexpected slip systems is found which does not coincide with the slip systems with the highest resolved shear stress. These unexpected slip systems are probably related to the dislocation nucleation process at the clamping point, which is influenced by the local curvature. [ABSTRACT FROM AUTHOR]

We report a novel approach to control the wavefronts of shear vertical (SV) waves in solids using metasurfaces constituted by a stacked array of composite plates, which are composed of two connecting parts made of different materials. The metasurfaces are connected at two ends to the half-space solids where the elastic SV waves propagate. The incident SV waves in the left half-space solid induce flexural waves in the composite plates and subsequently are converted back to SV waves in the right half-space solid. The time delay of flexural waves in each composite plate of the metasurfaces is tuned through the varying length of the two connecting components. To quantitatively evaluate the time delay in each composite plate, a theoretical model for analyzing the phase of the transmitted SV waves is developed based on the Mindlin plate theory. To control the SV waves at will, each composite plate in the metasurface is delicately designed according to the proposed theoretical model. For illustrative purposes, two metasurfaces are designed and numerically validated. [ABSTRACT FROM AUTHOR]

How carbon nanotubes (CNTs) interact with substrates is fundamental for understanding their physical properties. In existing theoretical and modeling studies, the substrates are considered to be rigid with semi-infinite thickness. In this work, the effects of finite substrate thickness and elasticity are analyzed theoretically and numerically for free boundary conditions. Based on the energy-variational approach, considering the interfacial van der Waals interactions and bending strain energies stored in CNTs and substrates, the governing equations and boundary conditions are derived analytically. The theoretical predictions are in reasonable agreement with the results of molecular dynamics simulations. When the substrate is sufficiently thick, the results of the present theoretical model are entirely consistent with previous models for the infinite-thickness substrate. However, for relatively thin substrates, the effect of substrate thickness is significant due to the geometric large deformation. Three stable adhesive states (initial non-adhesive, partially adhesive, and fully wrapping states) can be achieved, dependent on the substrate thickness, the number of CNT walls, and the interfacial adhesion work. The stability of adhesive configurations is explored by analyzing the energy variations corresponding to the adhesive deformation. We show that there exist several modes of energy variations, depending on the adhesion work and the substrate-CNT bending stiffness ratio, which exhibit linear and nonlinear influences, respectively. Our results could serve as guidelines to design CNT-on-substrate systems. [ABSTRACT FROM AUTHOR]

We have performed high pressure-temperature Brillouin scattering measurements on single crystal hydrogen sulfide using externally heated diamond anvil cell techniques. The pressure dependences of the acoustic velocities, isothermal elastic constants, and moduli of single crystal hydrogen sulfide have been determined along four isotherms. Both elastic constants and moduli increase monotonously with pressure along each isotherm, while they show a decreased tendency with temperature elevated under the same pressure points. The experimental equation of state of single crystal hydrogen sulfide is obtained by fitting with a third-order Birch-Murnaghan and Tait equation. It is proposed that the effect of hydrogen bonds contributes to the unique tendency of elastic anisotropy in single crystal hydrogen sulfide. Through our work, we have extended the melting curve and phase diagram of hydrogen sulfide up to 12 GPa and 580 K. [ABSTRACT FROM AUTHOR]

Isothermal and adiabatic shear moduli have been measured countless times. Adiabatic shear moduli which are generally considered to be the same as isothermal shear moduli are shown here to be unstable, so they cannot exist. A constitutive law that avoids adiabatic moduli is found to apply to polycrystalline isotropic solids. The equation is a power law in the volume per unit mass time the shear modulus. The volume is in turn a function of temperature T and pressure p in the system. The adiabatic moduli are established in shear stress versus strain space using a construction from isothermal elastic shear moduli. The derivation of this law replaces adiabatic with isochoric conditions in linear elastic, sheared solids. It is widely reported that the shear thermal expansion coefficient is zero since isotropic solids do not change the shape when heated. All solids with applied shear stresses and temperature dependent shear moduli change the shape and have shear thermal expansion coefficients. The thermal expansion coefficient is coupled into the shear component of the entropy and the T dependence of the isothermal shear modulus. In a sheared solid, only the single point τ = 0, γ = 0 has no shear entropy contributions and no thermal expansion and is mechanically unstable in adiabatic constructions. The exact form of the proposed constitutive law is based on solutions from a second order differential equation based on shear contributions from the entropy. [ABSTRACT FROM AUTHOR]

In this paper, we carry out an analytical study to investigate the dispersive and non-reciprocal properties of harmonic elastic wave propagation in a membrane on an elastic foundation. One side of the membrane is in contact with a uniform inviscid and incompressible flow. The analysis shows that the frequency spectrum and the dispersion curve are not symmetric, therefore breaking the principle of reciprocity. We show that the dynamics of the wave propagation of the system depends on the dimensionless phase velocity of the membrane and the dimensionless stiffness of the elastic foundation. The system possesses one region where the phase velocity of the propagating waves in opposite directions is different, and another where the waves travel only in one direction (directional band gap). There also exist regions in which only evanescent and spatially growing waves are excited. [ABSTRACT FROM AUTHOR]

We propose a comprehensive analytical theory for the description of versatile hysteretic phenomena in a graphene field effect transistor (GFET). Our theory account for the existence of the three most important rival factors, such as external dipoles on graphene free surface, localized states at the graphene-substrate interface, and the bound polarization charge coming from a ferroelectric substrate. In particular, we demonstrated that the absorbed dipole molecules (e.g., dissociated or highly polarized water molecules) can cause hysteretic form of carrier concentration as a function of gate voltage and corresponding dependence of graphene conductivity in GFET on the substrate of different types, including the most common SiO2 and ferroelectric ones. It was shown that the increase in the gate voltage sweeping rate leads to the complete vanishing of hysteresis for GFET on SiO2 substrate as well as for GFET on ferroelectric substrate for applied electric fields E less than the critical value Ec. For E>Ec, the cross-over from the anti-hysteresis to hysteresis take place. The carriers’ trapping from the graphene channel by the interface states describes the “antihysteresis” in GFET on PZT substrate well enough. These results well correlate with the available experimental data up to the quantitative agreement. So, the obtained analytical results predict new and clarify existing effects in GFET. They describe quantitatively the physical principles of GFET operation and can become the first necessary step to transform the state-of-art from almost empirical to analytical level, because they can be directly applied to describe the basic characteristics of advanced non-volatile ultra-fast memory devices using GFET on versatile substrates. [ABSTRACT FROM AUTHOR]

Successful wafer-scale layer transfer from high-quality 2-in. diameter bulk gallium nitride substrates was demonstrated using the Controlled Spalling technique. The crystal quality of both the as-fractured bulk substrate and the spalled GaN film was assessed using transmission electron microscopy analysis, and the defect density was below the detection limit (mid 107 cm−2) for both samples. By using the experimentally determined critical conditions for tensile stress and thickness of the Ni stressor layer, an effective fracture toughness KIC of 1.7 MPa √m could be calculated for [0001] fracture using the Suo and Hutchinson mechanical model. The resulting in-plane contraction of the GaN film after spalling permitted a novel method for measuring film strain without knowledge of the elastic properties of the material. This was used to measure the Raman E2(high) peak shift coefficient of Δω(cm−1) = 1411ε which, when converted to a stress coefficient (2.95 cm−1/GPa), was in agreement with only one other literature value. [ABSTRACT FROM AUTHOR]

Correlatively employing density functional theory and experiments congregated around high power pulsed magnetron sputtering, a plasma-surface model for metastable Cr0.8Al0.2N (space group Fm3...m) is developed. This plasma-surface model relates plasma energetics with film composition, crystal structure, mass density, stress state, and elastic properties. It is predicted that N Frenkel pairs form during Cr0.8Al0.2N growth due to high-energy ion irradiation, yielding a mass density of 5.69 g cm-3 at room temperature and Young’s modulus of 358–130 GPa in the temperature range of 50–700K for the stress-free state and about 150 GPa larger values for the compressive stress of 4 GPa. Our measurements are consistent with the quantum mechanical predictions within 5% for the mass density and 3% for Young’s modulus. The hypothesis of a stress-induced Young’s modulus change may at least in part explain the spread in the reported elasticity data ranging from 250 to 420 GPa. [ABSTRACT FROM AUTHOR]

By analyzing the magnetic energy, we investigated the deformation of magnetic chiral structures and derived estimates of the skyrmion lattice (SkL) elastic moduli and SkL Poisson's ratio. We verified that the SkL system is close to an elastically isotropic system in which skyrmions display a particle behavior with only nearest-neighbor interactions. We found that with the applied external field, the SkL shear modulus decreases and SkL Poisson's ratio increases. We also obtained an estimate for the critical energy required for the crystal axis reorientation of the SkL, which like the SkL shear modulus also decreases with the external field. These trends indicate that the SkL becomes soft and less solid as the external field increases until the chiral structures disappear at the critical field. [ABSTRACT FROM AUTHOR]

Flexoelectricity is the generation of electric polarization by the application of a non-uniform mechanical strain field, i.e., a strain gradient. This phenomenon is exhibited by all elastic dielectrics, but is expected to be significant only at very small scales. Energy harvesting is a potential future application area of flexoelectricity to enable next-generation ultra-low-power MEMS/NEMS devices by converting ambient vibrations into electricity. In this paper, an electroelastodynamic framework is presented and analyzed for flexoelectric energy harvesting from strain gradient fluctuations in centrosymmetric dielectrics, by accounting for the presence of a finite electrical load across the surface electrodes as well as two-way electromechanical coupling, and capturing the size effect. The flexoelectric energy harvester model is based on the Euler-Bernoulli beam theory and it assumes the main source of polarization to be static bulk flexoelectricity. Following recent efforts on the converse flexoelectric effect in finite samples, the proposed model properly accounts for thermodynamically consistent, symmetric direct and converse coupling terms. The transverse mode flexoelectric coupling coefficient (k) is obtained analytically as a direct measure of energy conversion; its dependence on the cantilever thickness and a material Figure of Merit (FoM) is shown. Size effects are further demonstrated by simulations of the electromechanical frequency response for a Strontium Titanate (STO) energy harvester at different geometric scales. It is obtained that the flexoelectric coupling coefficient of an STO cantilever for the fundamental bending mode increases from k ≈ 3:5 × 10-7 to k ≈ 0:33 as the thickness is reduced from mm- to nm-level. A critique of the experimentally identified large flexoelectric coefficient for Barium Strontium Titanate (BST) from the literature is also given with a coupling coefficient perspective. [ABSTRACT FROM AUTHOR]

Dielectric, elastic, and piezoelectric constants, and their corresponding losses are defined under constant conditions of two categories; namely, intensive (i.e., E, electric field or T, stress), and extensive (i.e., D, dielectric displacement or x, strain) ones. So far, only the intensive parameters and losses could be measured directly in a k31 mode sample. Their corresponding extensive parameters could be calculated indirectly using the coupling factor and "K" matrix. However, the extensive loss parameters, calculated through this indirect method, could have large uncertainty, due to the error propagation in calculation. In order to overcome this issue, extensive losses should be measured separately from the measurable intensive ones in lead-zirconate-titanate (PZT) k31 mode rectangular plate ceramics. We propose a new mechanical-excitation methodology, using a non-destructive testing approach by means of a partial electrode configuration, instead of the conventional full electrode configuration. For this purpose, a non-electrode sample was prepared, where the electrode covered only 10% of the top and bottom surfaces at the center to actuate the whole sample, and also monitor the responding vibration. The admittance spectrum of this sample, corresponds to PZT properties under dielectric displacement D constant condition. Furthermore, ceramics with partial-electrodes were also prepared to create short and open circuit boundary conditions, attributing to resonance and anti-resonance modes. In the proposed way, we were able to measure both intensive and extensive elastic compliances and mechanical losses directly for the first time. The accuracy of this new method is compared with the conventional measurements by use of indirect calculations. The preliminary results (by neglecting the 10% actuator part difference at this point) were obtained, which were in good agreements (less than 3% difference) with the previous indirect method. [ABSTRACT FROM AUTHOR]

The obscure nature of glass physics has led to develop various correlations between different parameters and properties of metallic glasses. Despite these correlations, the clear picture of plastic deformation is still lacking. We have measured elastic recovery in metallic glasses by indentation, and found the elastic recovery correlate with different properties and parameters of metallic glasses. All these observations can be quite well explained with flow unit model which could provide clearer picture on the plastic deformations and nature of the metallic glasses. [ABSTRACT FROM AUTHOR]

The thickness of carbon nanotubes is an important issue for the characterization and design of these structures. In this article, thickness free expressions for the shear modulus of single-walled carbon nanotubes have been developed by finite element simulations on the minimum potential energy circle. As a part of this work, some equations have been obtained to define the relation between the thickness and the shear modulus, which are in good agreement with previous studies. Moreover, these expressions are in good agreement with both continuum and quantum mechanics and capable to support "Yakobson's paradox," that the scattering data for the elastic properties of carbon nanotubes are due to the not-well-defined thickness for these structures. Furthermore, these expressions can provide a tool for the prediction of the shear modulus of single-walled carbon nanotubes in regards to any thickness assumption when the experimental investigations are too difficult to realize. [ABSTRACT FROM AUTHOR]

The propagation of traveling Lamb wave in single layer of elastic metamaterial is investigated in this paper. We first categorized the traveling Lamb wave modes inside an elastic metamaterial layer according to different combinations (positive or negative) of effective medium parameters. Then the impacts of the frequency dependence of effective parameters on dispersion characteristics of traveling Lamb wave were studied. Distinct differences could be observed when comparing the traveling Lamb wave along an elastic metamaterial layer with one inside the traditional elastic layer. We further examined in detail the traveling Lamb wave mode supported in elastic metamaterial layer, when the effective P and S wave velocities were simultaneously imaginary. It was found that the effective modulus ratio is the key factor for the existence of special traveling wave mode, and the main results were verified by FEM simulations from two levels: the level of effective medium and the level of microstructure unit cell. [ABSTRACT FROM AUTHOR]

The formation of a new compound with stoichiometry As4O6·2He at relatively low pressure (3 GPa) has been recently reported when arsenolite (As4O6) powder is compressed with helium as a pressure-transmitting medium. In this work, we study the lattice dynamics of As4O6 and As4O6·2He at high pressures from an experimental and theoretical perspective by means of Raman scattering measurements and ab initio calculations and report the theoretical elastic properties of both compounds at high pressure. Raman scattering measurements show a completely different behaviour of As4O6 and As4O6·2He at high pressures. Furthermore, the theoretical calculation of phonon dispersion curves and elastic stiffness coefficients at high pressure in both compounds allow us to discuss their dynamical and mechanical stability under hydrostatic compression. Both compounds are dynamically stable even above 35 GPa, but As4O6 becomes mechanically unstable at pressures beyond 19.7 GPa. These results allow explaining the pressure-induced amorphization of As4O6 found experimentally above 15-20 GPa and the lack of observation of any instability in As4O6·2He up to the highest studied pressure (30 GPa). [ABSTRACT FROM AUTHOR]

Elastic interactions in GaAs/Si bilayer composite structures were studied by optically pumped nuclear magnetic resonance (OPNMR). The composites were fabricated by epoxy bonding of a single crystal of GaAs to a single crystal of Si at 373 K followed by selective chemical etching of the GaAs at room temperature to obtain a series of samples with GaAs thickness varying from 37 μm to 635 μm, while the Si support thickness remained fixed at 650 μm. Upon cooling to below 10 K, a biaxial tensile stress developed in the GaAs film due to differential thermal contraction. The strain perpendicular to the plane of the bilayer and localized near the surface of the GaAs was deduced from the quadrupolar splitting of the Gallium-71 OPNMR resonance. Strain relaxation by bowing of the composite was observed to an extent that depended on the relative thickness of the GaAs and Si layers. The variation of the strain with GaAs layer thickness was found to be in good agreement with a general analytical model for the elastic relationships in composite media. [ABSTRACT FROM AUTHOR]

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique to solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube- beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results. [ABSTRACT FROM AUTHOR]

We present the design for an acoustic system that can achieve particle trapping and transport using the acoustic force field above a phononic crystal plate. The phononic crystal plate comprised a thin brass plate with periodic slits alternately embedded with two kinds of elastic inclusions. Enhanced acoustic transmission and localized acoustic fields were achieved when the structure was excited by external acoustic waves. Because of the different resonant frequencies of the two elastic inclusions, the acoustic field could be controlled via the working frequency. Particles were transported between adjacent traps under the influence of the adjustable acoustic field. This device provides a new and versatile avenue for particle manipulation that would complement other means of particle manipulation. [ABSTRACT FROM AUTHOR]

Atomic level flow plays a critical role in the mechanical behavior of metallic glass (MG) while the connection between the flow and the heterogeneous microstructure of the glass remains unclear. We describe the heterogeneity of MGs as the elastic matrix with "inclusions" of nano-scale liquidlike flow units, and the plastic flow behavior of MGs is considered to be accommodated by the flow units. We show that the model can explain the various deformation behaviors, the transformation from inhomogeneous deformation to homogeneous flow upon strain rate or temperature, and the deformation map in MGs, which might provide insights into the flow mechanisms in glasses and inspiration for improving the plasticity of MGs. [ABSTRACT FROM AUTHOR]

Studies of the phase diagram of uranium have revealed a wealth of high pressure and temperature phases. Under ambient conditions the crystal structure is well defined up to 100 gigapascals (GPa), but very little information on thermal conduction or elasticity is available over this same range. This work has applied ultrasonic interferometry to determine the elasticity, mechanical, and thermal properties of depleted uranium to 4.5 GPa. Results show general strengthening with applied load, including an overall increase in acoustic thermal conductivity. Further implications are discussed within. This work presents the first high pressure studies of the elasticity and thermal properties of depleted uranium metal and the first real-world application of a previously developed containment system for making such measurements. [ABSTRACT FROM AUTHOR]

Compressional and shear wavevelocities of the α phase of hafnium have been measured up to 10.4GPa at room temperature using ultrasonic interferometry in a multi-anvil apparatus. A finite strain equation of state analysis yielded Ks0=110.4(5)GPa,G0= 54.7(5)GPa,K's0 = 3.7,andG'0 = 0.6Ks0 = 110.4(5)GPa,G0= 54.7(5)GPa,Ks0' = 3.7,andG0' = 0.6 for the elastic bulk and shear moduli and their pressure derivatives at ambient conditions. Complementary to the experimental data, the single crystal elastic constants, the elastic anisotropy, and the unit cell axial ratio c/a of α-hafnium at high pressures were investigated by Density Functional Theory(DFT) based first principles calculations. A c/a value of 1.605 is predicted for α-Hf at 40GPa, which is in excellent agreement with previous experimental results. The low-pressure derivative of the shear modulus observed in our experimental data up to 10GPa was found to originate from the elastic constant C44, which exhibits negligible pressure dependence within the current experimental pressure range. At higher pressures (>10GPa), C44 was predicted to soften and the shear wavevelocity νS trended to decrease with pressure, which can be interpreted as a precursor to the α-ω transition similar to that observed in other group IV elements (titanium and zirconium). The acoustic velocities, the bulk and shear moduli, and the acoustic Debye temperature (θD = 240.1KθD=240.1K) determined from the current experiments were all compared well with those predicted by our theoretical DFT calculations. [ABSTRACT FROM AUTHOR]

Previous reports of rapid phase transformation above 18 GPa [Erskine and Nellis, Nature 349, 317 (1991)] and large elastic waves below 18 GPa [Lucas et al., J. Appl. Phys. 114, 093515 (2013)] for shock-compressed ZYB-grade highly oriented pyrolytic graphite (HOPG), but not for less oriented ZYH-grade HOPG, indicated a link between the orientational order dependence of the HOPG response above and below the phase transformation stress. To gain insight into this link and into the mechanical response of HOPG shocked to peak stresses approaching the phase transformation onset, the compressibility of ZYB- and ZYH-grade HOPG in the shocked state was examined using front surface impact experiments. Particle velocity histories and sound velocities were measured for peak stresses reaching 18 GPa. Although the locus of the measured peak stress-particle velocity states is indistinguishable for the two grades of HOPG, the measured sound velocities in the peak state reveal significant differences between the two grades. Specifically (1) the measured sound velocities are somewhat higher for ZYH-grade HOPG compared with ZYB-grade HOPG; (2) the measured sound velocities for ZYH-grade HOPG increase smoothly with compression, whereas those for ZYB-grade HOPG exhibit a significant reduction in the compression dependence from 12 GPa to 17GPa and an abrupt increase from 17GPa to 18 GPa; and (3) the longitudinal moduli, determined from the measured sound velocities, are smaller than the calculated bulk moduli for ZYB-grade HOPG shocked to peak stresses above 15 GPa, indicating the onset of an elastic instability. The present findings demonstrate that the softening of the longitudinal modulus (or elastic instability) presented here is linked to the large elastic waves and the rapid phase transformation reported previously—all observed only for shocked ZYB-grade HOPG. The elastic instability in shocked ZYB-grade HOPG is likely a precursor to the rapid phase transformation observed above 18 GPa for this HOPG grade. [ABSTRACT FROM AUTHOR]

The transformation of diamond-cubic silicon to the metallic β-Sn phase is known to be "sluggish," even when the critical pressure (∼11 GPa) for the transformation is reached. In this letter, we use nanoindentation to apply pressures to just above the critical threshold. In this regime, the sample displays purely elastic behavior at zero hold time. As the hold time at maximum load is increased up to 180 s, the percentage of indents that plastically deform also increase. Interestingly, the indents deform via one of two distinct processes: either via a phase transformation to a mixed bc8/r8-Si end phase, or by initiation of crystalline defects. Raman spectroscopy and cross-sectional transmission electron microscopy are used to show that the two deformation mechanisms are mutually exclusive under the indentation conditions presented here, and elastic modelling was utilized to propose a model for this mutually exclusive behavior. Hence, this behavior enhances the potential for application of the exotic bc8/r8-Si end phase. [ABSTRACT FROM AUTHOR]